Astronomy & Astrophysics manuscript no. 13881 c ESO 2018 May 28, 2018 Kinematic parameters and membership probabilities of open clusters in the Bordeaux PM2000 catalogue⋆ A. Krone-Martins1,2 , C. Soubiran2 , C. Ducourant2,1 , R. Teixeira1,2 and J. F. Le Campion2 1 Instituto de Astronomia, Geof´ısica e Ciˆencias Atmosf´ericas, Universidade de S˜ao Paulo, Rua do Mat˜ao, 1226, Cidade Universit´aria, 05508-900 S˜ao Paulo-SP, Brazil 2 Observatoire Aquitain des Sciences de l’Univers, Laboratoire d’Astrophysique de Bordeaux, CNRS-UMR 5804, BP 89, 33271 Floirac Cedex, France Received 16 December 2009 / Accepted 16 February 2010 ABSTRACT Aims. We derive lists of proper-motions and kinematic membership probabilities for 49 open clusters and possible open clusters in the zone of the Bordeaux PM2000 proper motion catalogue (+11◦ ≤ δ ≤ +18◦). We test different parametrisations of the proper motion and position distribution functions and select the most successful one. In the light of those results, we analyse some objects individually. Methods. The segregation between cluster and field member stars, and the assignment of membership probabilities, is accomplished by applying a new and fully automated method based on both parametrisations of the proper motion and position distribution func- tions, and genetic algorithm optimization heuristics associated with a derivative-based hill climbing algorithm for the likelihood optimization. Results. We present a catalogue comprising kinematic parameters and associated membership probability lists for 49 open clusters and possible open clusters in the Bordeaux PM2000 catalogue region. We note that this is the first determination of proper motions for five open clusters. We confirm the non-existence of two kinematic populations in the region of 15 previously suspected non-existent objects. Key words. Galaxy: open clusters and associations, Methods: data analysis, Methods: statistical 1. Introduction distance, age, and metallicity. This membership determination is traditionally performed using the stellar kinematics, but in prin- Once the problem of selecting their physical members is re- ciple one could use a multidimensional space, using for exam- solved, open clusters are widely respected to be a most valu- ple, spatial and kinematic information, as in Zhao et al. (2006), able tool for undertaking studies of our Galaxy and stellar as- or CMD-isochrone information, as in Kharchenko et al. (2005). trophysics. These objects have been used, for example, to de- Nonetheless, we argue that, when analysing these objects, one termine the spiral structure of the Galaxy and investigate star should rely more on kinematics and as little as possible on a formation and evolution processes. They are particularly impor- single age CMD-based model analysis as in the aforementioned tant as tracers of the dynamics (Frinchaboy & Majewski 2008) study. This is because, as it has been reported in the litera- and the chemical evolution of our Galaxy’s disk (Friel 1995). In ture, the star formation in some open clusters could be non- the advent of high precision astrophysical surveys such as Gaia coeval,as seems to be true in NGC 3603(Eisenhauer et al. 1998) (Perryman et al. 2001), their contribution to astrophysical stud- and 14 other open clusters (Strobel 1992). An indication of an ies should become increasingly important. abundance spread has been reported for one of these objects However, to establish a coherent understanding of our (Frinchaboy et al. 2008). arXiv:1006.0096v1 [astro-ph.GA] 1 Jun 2010 Galaxy, one needs to use a significant number of open clusters Based on these results, we undertook a purely kinematic de- with consistently measured astrophysical parameters, and there termination of open cluster membership probabilities for objects have been numerous efforts in this direction (Kharchenko et al. located in the zone covered by the high precision proper mo- 2005; Bragaglia & Tosi 2006; Frinchaboy & Majewski 2008). tion catalogue PM2000 (Ducourant et al. 2006). We used a fully However, as noted by Frinchaboy & Majewski (2008), the inac- automated optimization method and a set of modified parametri- curacy of current membership determinations poses difficulties sations for the probability distribution functions based on Zhao in conducting these studies on a large scale. et al. (1990, 2006). The main advantage of using open clusters in these studies This paper is organisedas follows. In Sect. 2, we describe the is that once the complex problem of stellar membership is re- data we used and its selection process. In Sect. 3, we present the solved one can derive their main physical parameters such as methodology and algorithms chosen to obtain the membership Send offprint requests to: [email protected] lists and the cluster kinematic parameters.In Sect. 4, we describe ⋆ The Tables 1, 4, and 5 are available in electronic form at the CDS the validation of the method. In Sect. 5 we present our results, via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or and our comment on some individual objects. Finally, in Sect.6 via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/ we present the conclusions of our current study. 2 Krone-Martins et al.: Kinematics and membership of PM2000 zone open clusters 2. Data and CDS’s vizquery tool. Table 1 shows the input list of clusters that we used, as well as the class that we assigned to each object. 2.1. The PM2000 catalogue The data used to obtain the cluster kinematical parameters were selected from the extracted data by rejecting on the basis The PM2000 catalogue (Ducourant et al. 2006) is a proper mo- −1 tion catalogue that comprises about 2.6 million stars in the dec- of proper motion errors (ǫµ ≤ 6.0 mas yr ) and the total proper −1 lination zone +11◦ ≤ δ ≤ +18◦ and contains positions and motion (|µ| < 30.0 mas yr ). This was justified since high µ proper motions on the ICRS (International Celestial Reference field stars cause the proper motion distribution to be flattened, as System), as well as meridian magnitudes VM. It was derived previously noted in the literature (Balaguer-N´u˜nez et al. 2004b, from the compilation of systematic drift-scan observations in and references therein). Nonetheless, we computed membership the Bordeaux Carte du Ciel Zone with the Bordeaux auto- probabilities for all the stars in the extracted zones. mated meridian circle (Viateau et al. 1999) carried out over four years, the reduction of 512 Carte du Ciel plates (epoch 3. Methods t ≈ 1900) of the Bordeaux zone (Rapaport et al. 2001) scanned at the APM Cambridge, and the catalogues AC2000.2 (t ≈ 3.1. Mathematical model 1907), USNO-A2.0 (t ≈ 1950) and the unpublished USNO The traditional way of conducting membership assignment orig- Yellow Sky (YS3, t ≈ 1978). The positional precision ranges inates in the seminal works of Vasilevskis et al. (1958) and from 50 to 70 mas, while the proper-motion precision varies −1 Sanders (1971). Those two works provided the basic ideas for from 1.5 to 6 mas yr , depending on the magnitude. All the developing parametric membership analysis. The derived math- data was analysed using a global iterative astrometric reduc- ematical model is based on the assumptions that there are two tion (Teixeira et al. 1992; Benevides-Soares & Teixeira 1992; distinct kinematic populations in the observational field of the Ducourant & Rapaport 1991). cluster and that the proper motion distributions of those two pop- The catalogue is complete to VM = 15.4, with a limit- ulations can be parametrised by bivariate Gaussians. ing magnitude of VM = 16.2, and typical error of 0.03 mag In these studies, an elliptical function was used to describe (9.5 ≤ VM ≤ 13.5). In addition, a cross identification between the field population’s proper motion, while a circular one was all sources in the PM2000 and 2MASS (Cutri et al. 2003) was used for the cluster. Nonetheless, if either an external gravita- performed, so the PM2000 catalogue also includes 2MASS pho- tional influence or tidal effects were to act on different parts of tometry information for its objects. the cluster, the cluster’s proper motion distribution could be sig- nificantly affected, causing it to deviate from a circular function. 2.2. The clusters sample For this reason, we tested four parametrisations of the probabil- ity distribution functions (PDF) in this study. The starting point of our analysis is a list of 49 open clusters We adopted three variations of the general form of the PDF inside the PM2000 declination zone found in the D07 catalogue established by Zhao & He (1990) to take account of the obser- (Dias et al. 2002a). We performeda visual inspection of all these vational errors in each individual point. The proper-motion dis- clusters by using the Aladin Sky Atlas (Bonnarel et al. 2000) to persion parameters obtained from these PDFs are therefore the verify their coordinates. During this visual check, we noticed cluster and field intrinsic ones, which are independent of the ob- that the clusters Berkeley 29, 43, 45, and 47 needed to be slightly servational errors in the proper motions. The first variationis a recentered about 3’25”, 3’39”, 1’13”, and 1’27”, respectively. circular distribution, which is the most accurate representation The objects were then separated into four different classes: of the PDF for a non-disturbed object with symmetric observa- A-reference, B-known, C-known without proper-motion determi- tion errors. The second variation is elliptical (allowing for the nation,and D-others (including doubtful objects). An object was correlation coefficient) and the last a PDF in which we assume classified as D and not C when one or moreof the following con- that the intrinsic dispersion cannot be observed because of the ditions applied: size of the errors (as adopted by Balaguer-N´u˜nez et al.